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Energy stable and high-order-accurate finite difference methods on staggered grids
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering. Department of Geophysics, Stanford University, CA, USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
Department of Geophysics, Stanford University, USA / Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA.
2016 (English)Report (Other academic)
Abstract [en]

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. , 27 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2016:17
National Category
Computational Mathematics Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-132454ISRN: LiTH-MAT-R--2016/17--SEOAI: oai:DiVA.org:liu-132454DiVA: diva2:1046014
Available from: 2016-11-11 Created: 2016-11-11 Last updated: 2016-11-24Bibliographically approved

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